Collider bias is common in obesity research and proposed a cause of the several obesity paradoxes shown in epi papers (survival advantage in obese vs lean people with chronic conditions such as heart failure and diabetes).
My understanding of collider bias: chronic conditions (e.g. diabetes) have several causes, for simplicity let’s say obesity and genes, and assume genes are stronger risk factors of both diabetes and mortality than obesity is. When conditioning on diabetes (D=1, by stratification, adjustment, or selection), a collider bias occurs and may distort the relation between the two causes of diabetes. This bias may or may not cause obesity to appear protective. If you have obesity, you may have gotten diabetes because of your obesity or because of your genes. If you are lean, you have gotten diabetes because of your genes - which are stronger predictors of mortality than obesity. Therefore, even though obesity in the gen pop is predictive of both diabetes and mortality, among those with diabetes, obesity appear to be protective for mortality.
Okay, I think I got this. But what about the other strata of diabetes (D=0) - can the same distorted relationship occur among non-diabetics? Let’s say you are non-diabetic, if you are obese, you do not have diabetes because of protective genes (as opposed to bad genes in the example above). If you are lean, you do not have diabetes either because you are not obese or because you have protective genes. So, as in the example above, obesity among non-diabetics may appear protective.
To clarify, my question is whether the bias occurs in just one of the strata or both strata of the variable you condition on, and why, how and under which circumstances?
Does anyone have any thoughts on this? Am I missing something?